Linear holonomy groups of algebraic solutions of polynomial differential equations
We consider the problem of realization of a linear subgroup of as the linear holonomy group of an algebraic curve which is a leaf of a foliation of .
Regular foliations along curves
Topological Classification and Bifurcations of Holomorphic Flows with Resonances in ...2.
Problèmes de modules pour les formes différentielles singulières dans le plan complexe.
Holomorphic foliations in certain holomorphically convex domains of
Singularités nilpotentes et intégrales premières.
This paper presents a classification of plane dicritical nilpotent singularities, i.e. singularities which have nilpotent linear part and infinitely many separatrices. In particular the existence of meromorphic first integrals is discussed. The same ideas are applied to other kind of dicritical singularities.
On dicritical foliations and Halphen pencils
The aim of this article is to provide information on the number and on the geometrical position of singularities of holomorphic foliations of the projective plane. As an application it is shown that certain foliations are in fact Halphen pencils of elliptic curves. The results follow from Miyaoka’s semipositivity theorem, combined with recent developments on the birational geometry of foliations.
Minimal sets of foliations on complex projective spaces
Fonctions et feuilletages Levi-Flat. Étude locale
We define the notion of CR equivalence for Levi-flat foliations and compare in a local setting these foliations to their linear parts. We study also the situation where the foliation has a first integral ; a condition is given so that this integral is the real part of a holomorphic function.
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